A numerical and linear study of modes driven toward instability by PN radiation-reaction force (current quadrupole) in slowly rotating neutron stars was presented. It consists in a time evolution using spectral methods in spherical coordinates for spatial operators. Whatever the noisy initial data, there exists a hydrodynamic instability. Yet, depending on the background, the symmetric properties of the mode may change. Thus, in a rigid rotating Newtonian star, the expected and purely axial r-mode1 is growing. But, when the Newtonian background is assumed to be differentially rotating or when the evolution is done in the framework of general relativity with Cowling approximation (frozen spacetime), a coupling between axial and polar modes appears. Then, the mode driven to instability no longer belongs to one of these subclasses. Preliminary results were presented, showing the common features and main differences between Newtonian and relativistic cases2.